HEATSOF ~ I I X I X OFG NONELECTROLYTE SOLUTIONS
1959
Heats of Mixing of Nonelectrolyte Solutions.
111.
Solutions of the
Five Hexane Isomers with Hexadecane'
by John A. Larkin, David V. Fenby, Theodore S. Gilman, and Robert L. Scott Contribution No. 1895 f r o m the Department of Chemistry, Unirersity of California, Los Angeles, California 90024 (Received January 4, 1966)
The heats of mixing for the five isomers of hexane and n-hexadecane at 25.00° have been measured. The maximum values (all very near z = 0.5) are 113.7, 184.0, 170.5, 236.0, and 187.5 joules moleF1 for n-hexadecane with n-hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, and 2,3-dimethylbutane, respectively. These measurements agree reasonably well with the predictions of the Scatchard-Hildebrand solubility parameter theory (i.e., with the square of the difference of the solubility parameters); they also can be correlated with the energies of vaporization of the hexane isomers.
Introduction The heats of mixing of normal saturated hydrocarbons have been extensively i n v e ~ t i g a t e d . ~ -We ~ have extended these studies to branched hydrocarbons and report here the heat of mixing ( i e . , the excess enthalpy BE) a t 25.00' of n-hexadecane with each of the five isomers of hexane. The n-CsH14 n-CleH34 system has been previously measured2s3p6although not a t 25'. Our results are compared with the ScatchardHildebrand solubility parameter theory' according to which the energy of mixing at constant volume ( i e . , the volume excess energy BVE)is dependent upon the solubility parameters of the two components. In recent studies8 involving solutions of the hexane isomers which are known not to conform to the solubility parameter theory, it has been found that the upper critical solution temperatures can be correlated well with the energies of vaporization of the hexane isomers. The heats of mixing reported here are studied with respect to these observations.
of about 100 cm of 36 B &- S heavy Formvar manganin wire (Driver-Harris Co.) wound noninductively onto a glass tube. The latter was then inserted into a glass pocket in the base of the mixing vessel and fixed in place with an epoxy resin. The leads from the mixing vessel to the external circuitry were of I/&. diameter copper wire. The galvanometer used by Larkin and McGlashan was replaced by a ListonBecker Breaker amplifier (Model 14) and a Varian recorder (Type G-10). Procedure. The experimental procedure was similar to that previously d e ~ c r i b e d the , ~ fall in temperature being compensated for as nearly as possible by the simultaneous introduction of a measured quantity of electrical energy. The primary source of error arises from the extrapolation of the temperature-time curves
Experimental Section Calorimetric Apparatus. The calorimeter was similar to that described in detail by Larkin and McGla~han.~ The mixing vessels used had four Veco (Victory Engineering Co.) Type 21A1 thermistors connected in parallel over the surface using 0.005-in. diameter platinum wire. The heater was constructed
(4) M. L. RlcGlashan, K. W. Morcom, and A. G. Williamson, ibid., 57, 601 (1961). (5) M. L. McGlashan and K. W. hforcom, ibid., 57, 907 (1961). (6) G. Scatchard, L. B. Ticknor, J. R. Goates, and E. R. McCartney, J . Am. Chem. Soc., 74, 3721 (1952). (7) C f . J. H. Hildebrand and R. L. Scott, "Regular Solutions," Prentice-Hall, Inc., Englewood Cliffs, N. J . , 1962. (8) M.S.B. Munson, J . Phys. Chem., 68, 796 (1964). L.IhlcGlashan, . J . Chem. SOC.,3425 (1961). (9) J. A. Larkin and &
+
(1) This work was supported in part by the National Science Foundation. (2) J. H. van der Waals and J. J. Hermans, Rec. Traz. Chim., 69, 949 (1950). (3) RI. L. McGlashan and K. W. Morcom, Trans. Faraday Soc., 57, 581 (1961).
Volume 70, .)-umber 6 J u n e 1966
J. A. LARKIN,D. V. FENBY,T. S. GILMAN,AND R. L. SCOTT
1960
used to evaluate The calorimeter was tested peroxide formation. This complication was overcome by vigorously shaking some of the sample with mercury by making measurements on the system benzene carbon tetrachloride a t 25.00', the advantages of which for approximately 15 min and then distilling the 2as a test system have been extensively d i s c u s ~ e d . ~ J ~methylpentane from the mercury and black precipitate The results obtained are listed in Table I and are in under an atmosphere of dry nitrogen. The sample obsatisfactory agreement with those of Larkin and Mctained in this way was found to be quite inert to Glashan. Although our results tend to be somewhat mercury even after a period of several months. higher than those predicted using their eq 2, this The refractive indices of the samples used were tendency is also reported at the conclusion of ref 9. measured a t 25' using an Abbe refractometer (Erb and Gray) and are compared in Table I1 with literature values. As a further check of purity, an nmr spectrum was obtained for each sample at high amplification. Table I: Heats of Mixing of Benzene + Carbon These spectra indicated no appreciable amount of Tetrachloride a t 25.00' impurity.
+
ZCCI4
0.4003 0.4850 0.4868 0.4962 0.4985 0,4997 0.5005 0,5042 0.5994
joules mole-', this work
112.8 116.1 115.7 116,3 115.6 116.8 116.3 116.5 111.5
joules mdle -1. from eq 2 of ref 9
112.1 115.7 115.7 115.7 115.7 115.7 115.7 115.6 110.5
Materials. n-Hexadecane, Humphrey-Wilkinson ASThI grade (alcohol derived), was further purified by four fractional crystallizations (freezing point, 18.10') and dried over CaH2. The established purity (assuming 18.15' to be the correct freezing point and a heat of fusion of 12.7 kcal mole-') is better than 99 mole %. n-Hexane, Phillips 66 Research grade (Phillips Petroleum Co.), having a purity of 99.97 mole % was used without further purification. 2,2-Dimethylbutane, Phillips 66 Research grade, having a purity of 99.98 mole % was used without further purification. 2,3-Dimethylbutane, Phillips 66 Research grade, having a purity of 99.89 mole % was used without further purification. 3-Methylpentane, Phillips 66 Research grade, ha,ving a purity of 99.83 mole % was used without further purification. 2-Methylpentane, Phillips 66 Research grade, having a purity of 99.70 mole yowas used. Early experiments using this material showed that it gave a black precipitate with mercury. This was thought to be due to peroxide formation," although the producer indicates12 that under normal storage conditions it is not considered necessary to inhibit this material against The Journal of Physical Chemistry
Table I1 : Refractive Indices of n-Hexadecane and the Hexane Isomers a t 25' n2jD
n25D
Material
(measd)
n-Hexadecane n-Hexane
1.4322 1,3722
2-Methylpentane 3-Methy lpentane
1,3686 1,3737
2,2-Dimethylbutane
1.3658
2,3-Dimethylbutane
1,3721
I
(lit.)-
1,4325013 1.43247l'
1.3722613 1.3722914 1.3687313 1,3738613 1.3738914 1 .3659513 1.3659214 1.3723113
1 .3723014 1 .3722414 1 .373814 1 .3737614 I.3661l 4 1 .3658514 1.3721214
Results The results of our experiments at 25.00' for the five systems are given in Tables 111-VII. The composition is always expressed as the mole fraction, x 2 , of nhexadecane. The results were fitted by the method of least squares m
BE = z(l - z)Ch,(l - 2z)" n=O
(1)
to the expression using a computer program.15 Each result was weighted according to an estimated extrapolation error. It was found that the data did not warrant the use of more than two parameters although probably (10) hl. L. McGlashan, Pure A p p l . Chem., 8, 157 (1964). (11) "Oxidation Reactions of Hydrocarbons," Discussions Faraday SOC.,10 (1951). (12) Phillips Petroleum Co., private communication.
(13) "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," prepared by the American Petroleum Institute, Research Project 44; extant as of 1964. (14) J. Timmermans, "Physicochemical Constants of Pure Organic Compounds," Elsevier Publishing Co., Inc., New York, N. Y., 1950. (15) D.B. Myers and R. L. Scott, Ind. Eng. Chem., 55, 43 (1963).
1961
HEATSOF MIXINGOF NONELECTROLYTE SOLUTIONS
Table IV : Heats of Mixing for 250
2-Methylpentane
+ n-Hexadecane BE/
-
-
40
1
q, 0
150
-E Q)
E
'0
30
0 0
IO0
\
2o
50
k
IO
0 0.0
z2
joules mole-1
0.1972 0.3335 0.4166 0.4318 0.4996 0.5000 0.5050 0.5545 0.5769 0.6587 0.8336
113.5 164.0 179.6 180.4 186.9 182.7 184.2 180.5 179.1 164.9 102.9
-2.5 0.8 1.0 0.0 3.0 -1.2 0.3 -1.4 -0.7 -0.8 0.4
0
0,2
0.4
0.6
I .o
09
x2
+
Figure 1. Excess enthalpies at 25.00' of the systems n-C6H14 n-Cl&.a (0),2-methylpentane n - c d a t (a),3-methylpentane
+
+
e/
joules mole -1
3-Methylpentane
+ n-Hexadecane
+
n-C&4 ( x), 2,2-dimethylbutane n-Cl6H34 (A), 2J-dimethglbutane n-ClgH34 (+). The solid curves are calculated from eq 1 using the parameters given in Table VIII.
+
Table V : Heats of Mixing for
more would be needed if measurements nearer the extremities of the mole fraction range had been made. (See Figure 1 .) Table VI11 gives the values of the parameters ho and hl for the five systems. Also given are the standard deviations, u, defined in the usual way.15 Values of the excess, 8, of the measured values of RE over the values calculated using eq 1 with two parameters are shown in the last columns of Tables 111-VII.
RE/ 22
0.2053 0.3084 0.4310 0.4844 0.5351 0.6119 0.6590 0.7566
@/
joules mole -1
joules mole -1
114.3 148.5 166.8 171.2 168.8 161.7 148.7 129.1
2.6 2.6 -0.9 0.4 -1.3 -0.6 -4.9 3.3
Table VI : Heats of Mixing for n-Hexadecane 2,2-Dimethylbutane
+
Table 111: Heats of Mixing for %-Hexane
PE/
+ n-Hexadecane
xz
joules mole -1
0.3011 0.3118 0.3986 0.4647 0.4997 0,5084 0,5206 0.5573 0,5994 0,6953
95.1 97.6 109.2 113.5 113.7 113.2 113.3 113.1 109.0 100.0
-0.1 0.5 0.3 0.2 -0.3 -0.8 -0.6 0.4 -0.9 2.7
Our n-CeHle n-C16H34 results have a maximum a t xz = 0.50 compared with xz = 0.48 which the McGlashan and Morcom equation for RE (eq 1, ref 3) yields a t 25.00'. In this respect we are more in agree-
@/
joules mole-'.
joules mole -1
0.0518 0,1800 0.3105 0.3144 0.4642 0.4675 0.4904 0.5060 0.5590 0,6517 0.8059
58.7 150.7 211.3 208.0 235,9 235.5 232.2 234.6 230.2 208.5 139.3
7.6 1.3 0.7 -3.9 -0.4 -0.8 -3.8 -0.6 1.1 2.2 2.4
e/
joules mole -1
+
GE/
2 2
ment with van der Waals and Hermans.2 The maximum excess enthalpy (REmax= 114.1 joules mole-') that we obtain is a little higher than that predicted (REmax= 112.0 joules mole-l) using the McGlashan and Morcom equation. This is not unexpected as Volume 70. Number 6 June 1966
J. A. LARKIN,D. V. FENBY, T. S. GILMAN, AND R. L. SCOTT
1962
Table VII: Heats of Mixing for 2,3-Dimethylbutane n-Hexadecane
+
In Table IX we list the standard energy of vaporization, AEV, the molar volume, V, and the solubility parameter, 6, a t 25' for n-hexadecane and each of the hexane isomers. ABV is computed by subtracting RT from the standard heats of vaporization at 250.13 In Table X we list R E m a x for each of the five systems together with the corresponding xz ,max. These values are compared with EVEmax and XZ,mar predicted using eq 4 and 3, respectively. The agreement is quite good, especially considering that RE < O.1RT; ScottlBhas pointed out that this =tO.lRT is an approximate limit for the usefulness of solubility parameter theory.
e/
22
RE/ joules mole -1
joules mole -1
0.0653 0.1996 0,3014 0.4010 0.4809 0.4982 0.5082 0.5504 0.6055 0.7334 0.8192
43.9 125.7 163.5 180.6 185.4 183.5 184.9 186.7 176.3 145.1 108.6
-4.6 1.1 1.6 -1.6 -1.8 -3.5 -1.8 3.0 0.4 3.8 2.9
Table VIII" I/
oal mole-'
cel mole -1
0.8 1.6
109.0 175.9
-2.2 -1.1
0.2 0.4
1.0
2.7
163.4
0.3
0.6
942.3
109.5
2.1
225.2
26.2
0.5
747.8
53.5
2.1
178.7
12.8
0.5
+
455.9 735.8
-9.1 -4.6
+
683.7
+
+
n-Hexane n-C~H34 2-Methylpentane n-CleH~ 3-Methylpentane n-C16H34 2,2-Dimethylbutane n-C16& 2,3-Dimethylbutane n-C&4 a
hO/ os1 mole -1
h1/ joules mole -1
System
+
./
hl/
joules mole -1
h d joules mole -1
The experimental results are shown in Figure 1.
Larkin and McGlashang report that their type of calorimeter yielded for the CCl, CaHesystem higher results than did earlier calorimeters.
+
Table
IX AiV/ kcsl mole -1
Discussion According to the Scatchard-Hildebrand solubility parameter theoryJ7the molar energy of mixing a t constant volume (ie., the volume excess energy EVE)is given by
EVE=
+ x2V2)(61 -
(&
62)24142
(2)
in which xi, Vi, di, and 6i refer to the mole fraction, molar volume, volume fraction, and solubility parameter, respectively, of the component i. The solubility parameter is defined by 6i = (Agi/Vi)'" where AEVi is the molar energy of vaporization of i. From eq 2, the maximum EVEoccurs a t V11h 22
=
T71vz
+
r2vz
(3)
and has the magnitude which is shown above in eq 4. The Journal of Physical Chemistry
n-Hexadecane n-Hexane 2-Methylpentane 3-Methylpentane 2,Z-Dimethylbutane 2,3-Dimethylbutane
18.79 6.962 6.567 6.662 6.058 6.392
Fl
cm8 mole - 1
294,083 131.598 132.875 130.611 133,712 131,156
a/ cal'/z cm -a/z
8.00 7.27 7.03 7.14 6.73 6.98
+
Except in the case of n-hexane n-hexadecane," volumes of mixing of these systems are not yet available. Consequently, we are unable a t present to estimate the corrections arising from the volume changes accompanying mixing. It should be recalled (16) R. L. Scott, Ann. Rev. Phys. Chem., 7,43 (1956). (17) A. Desmyter and J. H. van der Waals, Rec. Trav. Chim., 77, 53 (1958).
HEATSOF MIXINGOF YONELECTROLYTE SOLUTIONS
1963
Table X : Comparison of Experimental Results with Solubility Parameter Theory Predictions 7Experiment-
HE,,,/ joules mole -1
+
n-Hexane ?&1&4 2-Methylpentanta n-C16Haa 3-Nethylpentane n-C~sHlc 2,2-Dimethylbutane n-CleH34 2,Y-Dimethylbutane n-Cd34
+ + + +
Theory (eq 3, 4) -@ma,/
xg,mSx
joules mole -1
114.1 184.0
0.50 0.50
105 187
0.40 0.40
170.5
0.51
146
0.40
236.0
0.47
321
0.40
187.5
0.47
205
0.40
~
2
,
~
~
.
y 3 0 6.0
6.2
6.4 6,6 6.8 10 k caI mole-' Figure 2. The maximum excess enthalpies, REmax, compared with the molar energies of vaporization of the hexane isomers.
A?/
that when the measurements of Morcom and McGlasham3 on n-hexane n-hexadecane are converted to a constant volume frame of referen~e,~ the volume excess energy, BvE, shows a maximum near x = 0.4 in agreement with the prediction of eq 3. This same conversion however yields approximately 270 joules mole-' for EVEmrtx in substantial disagreement with the 105joules mole-' predicted by eq 4. The upper critical solution temperatures, 1,) of the hexane isomers in a number of fluorochemicals have been ~ b t a i n e d . *As ~ ~is~ ~now ~ ~ well known, such solutions do not conform to the solubility parameter theory. ilIunson8 determined the upper critical solution temperatures for the hexane isomers in perfluorotributylamine and found that they correlated well with the energies of vaporization, ABv, of the hexane isomers. A similar correlation was found to hold in earlier investigations of four of the hexane isomers in perflu~roheptane'~ and all of the hexane isomers in n-perfluoropentane,'8 although in this latter case the linearity is not quite as striking. It is of some interest that in these three cases a plot of t, IJS. ABV apparently results in a better correlation than one of t, os. the cohesive energy density, ABV/P = 6*,most strikingly in the work of Illunson.8 In Figures 2 and 3 we have plotted REmaxagainst ABV and ABV/ p,respectively. There is considerable scatter in both cases, so one cannot claim better correlation in one case than the other. It should be noted that the correlation is the reverse of that with fluorochemicals, n-hexane being the best solvent (ie., has the smallest excess free energy) for n-hexadecane and the poorest for fluorochemicals. This, of course, is to be expected from the solubility parameter values, that of n-hexadecane being greater
+
i
55
50
\
0
2
140 35 E
25 49 51 @Ev/Vl/cat cm-3 47
53
55
compared Figure 3. The maximum excess enthalpies, REmax, with the cohesive energy densities of the hexane isomers.
than those of the hexane isomers whereas those of the fluorochemicals are smaller. Any more detailed analysis of the experimental results presented in this paper will require data on the volumes of mixing. We plan to measure the heats of mixing a t higher temperatures. Acknowledgment. D. V. F. gratefully acknowledges the award of a Postgraduate Scholarship in Science by the University Grants Committee, New Zealand. (18) R. Dunlap, R. Digman, and J. Vreeland, Abstracts, 124th National LMeeting of the American Chemical Society, Chicago, Ill., Sept 1953. (19) J. B. Hickman, J. Am. Chem. SOC.,77, 6154 (1955).
Volume 70, Xumber 6 June 1966
